Floatation/Buoyancy perspectives

Car Talk puzzler to wrap your head around buoyancy:

Tommy's Cubed Car

One day, Ray secretly takes Tom's beloved black 1965 AMC Ambassador convertible to the crusher, where it's transformed into a 3-by-3-by-3-foot solid cube of rust, headrests, and mice and placed on a garbage barge. While the barge is crossing a lake, it falls overboard. Assuming water can't escape from the lake, does the water level go up, go down, or stay the same?​

I'll post the answer tomorrow. Don't worry, the answer contains an explanation.

Methow Roamer

Seeker of the Exotic and Aquatic
The water level goes down.

While on the barge the car displaces an amount of water equal to it's own weight. It does this because it is pressing down on the barge which presses down into the water enough to displace a volume of water equal to the weight of the barge/car.
Remove the car from the barge and now it only displaces a volume of water equal to the weight of the barge.
The barge rises slightly, the water level goes down.

But then the car hits the water...
Water floods all the air space inside the cube and it sinks to the bottom of the lake. Now the car displaces a volume of water equal to the volume of the parts of the car. A given volume of steel is heavier than an equal volume of water so the car sinks.

When the car was on the barge it displaces a volume of water equal to it's weight. When the car is in the water it displaces a weight of water equal to it's volume.

Remove car from barge: water level drops equal to weight of car (water amount A)
Put car in lake: water level rises equal to volume of the car (water amount B)

Because water amount A is greater than water amount B the car floats on the barge.
Also because water amount A is greater than water amount B, the lake rises when the car falls in, but not as much as it lowered when the car fell off the barge.

Lake level goes down.

That's my take on the subject.


Just waiting on warmer weather, .......
One would think that with all factors considered, like if it is raining during this time period, or is the lake spring fed, or just where did the water that makes/creates the lake come from? in addition to the coefficient of friction, equaling the air mass that travels over the lake surface @ a given rate of wind velocity, or that the temperature changes in a 24 hour period does, or does not have any effect upon the evaporation rate @ a given set temperature. With all items matching exact conditions of the time & day of the cube falling into the water, the water level would rise in displacement of the weight of the sinking cube, measured one hour after the cube fell into the water, but if measured @ the same time as the cube fell into the water it would not affect the water level at all, because the weight was supported by the barge which displaced the same volume of water as the total of the two pieces together or separately. There will be different displacement values of the articles placed into the water but the water level will remain the same, but only because of the total weight placed into the water.

But following the story plot,

In which everything is okey-dokey until Tom find's out about Ray's betrayal, & kills off all of Ray's whole family by placing their bodies in another boat & driving it into the rocks @ max speed of the boat which Tom sprayed with fuel, the resulting explosion opens another investigation & all trains of thought about floatation & buoyancy are forgotten in the ensuing questioning of the local Coast Guard/FBI/DNR officers assigned to the wreck & deaths of Ray & his family.

...In which everything is okey-dokey until Tom find's out about Ray's betrayal, & kills off all of Ray's whole family...
Don't forget... they're brothers: http://www.cartalk.com/content/tom-and-rays-bios-photos-0

Here's the answer:

It went down. When the 3,000-pound cube is in the barge, it's displacing its weight in water. A cubic foot of water weighs about 62.4 pounds, so the barge displaced about 48 cubic feet (3,000 pounds of steel divided by 62.4 is about 48).

When the cube sinks, it displaces an amount of water equal to its volume. Since it's a 3-foot cube, that's 27 cubic feet. So the water level goes down about 21 cubic feet (48 minus 27 equals 21). Moments later, more cubic feet are displaced, as Tommy jumped in to try to save the sleek black beauty.​

Jim Wallace

Smells like low tide.
Yes! Now I understand the real reason Bob Triggs posted his weather warning....folks trapped indoors by the stormy weather comment on threads like this one!:rofl:

I'm getting out of here and heading out to my shop. Got projects!

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